///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
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/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
/// 
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
/// 
/// Restrictions:
///		By making use of the Software for military purposes, you choose to make
///		a Bunny unhappy.
/// 
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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/// THE SOFTWARE.
///
/// @ref gtx_matrix_decompose
/// @file glm/gtx/matrix_decompose.inl
/// @date 2014-08-29 / 2014-08-29
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

namespace glm {
    /// Make a linear combination of two vectors and return the result.
    // result = (a * ascl) + (b * bscl)
    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec3<T, P>
    combine(
            tvec3<T, P>
    const & a,
    tvec3<T, P> const &b,
            T
    ascl,
    T bscl
    ) {
    return (
    a *ascl
    ) + (
    b *bscl
    );
}

template<typename T, precision P>
GLM_FUNC_QUALIFIER void v3Scale(tvec3 <T, P> &v, T desiredLength) {
    T len = glm::length(v);
    if (len != 0) {
        T l = desiredLength / len;
        v[0] *= l;
        v[1] *= l;
        v[2] *= l;
    }
}

/**
* Matrix decompose
* http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
* Decomposes the mode matrix to translations,rotation scale components
*
*/

template<typename T, precision P>
GLM_FUNC_QUALIFIER bool decompose(tmat4x4 < T, P >
const & ModelMatrix,
tvec3 <T, P> &Scale, tquat<T, P>
& Orientation,
tvec3 <T, P> &Translation, tvec3<T, P>
& Skew,
tvec4 <T, P> &Perspective
)
{
tmat4x4 <T, P> LocalMatrix(ModelMatrix);

// Normalize the matrix.
if(LocalMatrix[3][3] == static_cast<T>(0))
return false;

for(
length_t i = 0;
i < 4; ++i)
for(
length_t j = 0;
j < 4; ++j)
LocalMatrix[i][j] /= LocalMatrix[3][3];

// perspectiveMatrix is used to solve for perspective, but it also provides
// an easy way to test for singularity of the upper 3x3 component.
tmat4x4 <T, P> PerspectiveMatrix(LocalMatrix);

for(
length_t i = 0;
i < 3; i++)
PerspectiveMatrix[i][3] = 0;
PerspectiveMatrix[3][3] = 1;

/// TODO: Fixme!
if(
determinant(PerspectiveMatrix)
== static_cast<T>(0))
return false;

// First, isolate perspective.  This is the messiest.
if(LocalMatrix[0][3] != 0 || LocalMatrix[1][3] != 0 || LocalMatrix[2][3] != 0)
{
// rightHandSide is the right hand side of the equation.
tvec4 <T, P> RightHandSide;
RightHandSide[0] = LocalMatrix[0][3];
RightHandSide[1] = LocalMatrix[1][3];
RightHandSide[2] = LocalMatrix[2][3];
RightHandSide[3] = LocalMatrix[3][3];

// Solve the equation by inverting PerspectiveMatrix and multiplying
// rightHandSide by the inverse.  (This is the easiest way, not
// necessarily the best.)
tmat4x4 <T, P> InversePerspectiveMatrix = glm::inverse(
        PerspectiveMatrix);//   inverse(PerspectiveMatrix, inversePerspectiveMatrix);
tmat4x4 <T, P> TransposedInversePerspectiveMatrix = glm::transpose(
        InversePerspectiveMatrix);//   transposeMatrix4(inversePerspectiveMatrix, transposedInversePerspectiveMatrix);

Perspective = TransposedInversePerspectiveMatrix * RightHandSide;
//  v4MulPointByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspectivePoint);

// Clear the perspective partition
LocalMatrix[0][3] = LocalMatrix[1][3] = LocalMatrix[2][3] = 0;
LocalMatrix[3][3] = 1;
}
else
{
// No perspective.
Perspective = tvec4<T, P>(0, 0, 0, 1);
}

// Next take care of translation (easy).
Translation = tvec3 < T, P
>(LocalMatrix[3]);
LocalMatrix[3] = tvec4<T, P>(0, 0, 0, LocalMatrix[3].w);

tvec3 <T, P> Row[3], Pdum3;

// Now get scale and shear.
for(
length_t i = 0;
i < 3; ++i)
for(
int j = 0;
j < 3; ++j)
Row[i][j] = LocalMatrix[i][j];

// Compute X scale factor and normalize first row.
Scale.
x = length(Row[0]);// v3Length(Row[0]);

v3Scale(Row[0],
static_cast<T>(1));

// Compute XY shear factor and make 2nd row orthogonal to 1st.
Skew.
z = dot(Row[0], Row[1]);
Row[1] =
combine(Row[1], Row[0],
static_cast<T>(1), -Skew.z);

// Now, compute Y scale and normalize 2nd row.
Scale.
y = length(Row[1]);
v3Scale(Row[1],
static_cast<T>(1));
Skew.z /= Scale.
y;

// Compute XZ and YZ shears, orthogonalize 3rd row.
Skew.
y = glm::dot(Row[0], Row[2]);
Row[2] =
combine(Row[2], Row[0],
static_cast<T>(1), -Skew.y);
Skew.
x = glm::dot(Row[1], Row[2]);
Row[2] =
combine(Row[2], Row[1],
static_cast<T>(1), -Skew.x);

// Next, get Z scale and normalize 3rd row.
Scale.
z = length(Row[2]);
v3Scale(Row[2],
static_cast<T>(1));
Skew.y /= Scale.
z;
Skew.x /= Scale.
z;

// At this point, the matrix (in rows[]) is orthonormal.
// Check for a coordinate system flip.  If the determinant
// is -1, then negate the matrix and the scaling factors.
Pdum3 = cross(Row[1], Row[2]); // v3Cross(row[1], row[2], Pdum3);
if(
dot(Row[0], Pdum3
) < 0)
{
for(
length_t i = 0;
i < 3; i++)
{
Scale.x *= static_cast<T>(-1);
Row[i] *= static_cast<T>(-1);
}
}

// Now, get the rotations out, as described in the gem.

// FIXME - Add the ability to return either quaternions (which are
// easier to recompose with) or Euler angles (rx, ry, rz), which
// are easier for authors to deal with. The latter will only be useful
// when we fix https://bugs.webkit.org/show_bug.cgi?id=23799, so I
// will leave the Euler angle code here for now.

// ret.rotateY = asin(-Row[0][2]);
// if (cos(ret.rotateY) != 0) {
//     ret.rotateX = atan2(Row[1][2], Row[2][2]);
//     ret.rotateZ = atan2(Row[0][1], Row[0][0]);
// } else {
//     ret.rotateX = atan2(-Row[2][0], Row[1][1]);
//     ret.rotateZ = 0;
// }

T s, t, x, y, z, w;

t = Row[0][0] + Row[1][1] + Row[2][2] + 1.0;

if(t > 1e-4)
{
s = 0.5 / sqrt(t);
w = 0.25 / s;
x = (Row[2][1] - Row[1][2]) * s;
y = (Row[0][2] - Row[2][0]) * s;
z = (Row[1][0] - Row[0][1]) * s;
}
else if(Row[0][0] > Row[1][1] && Row[0][0] > Row[2][2])
{
s = sqrt(1.0 + Row[0][0] - Row[1][1] - Row[2][2]) * 2.0; // S=4*qx
x = 0.25 * s;
y = (Row[0][1] + Row[1][0]) / s;
z = (Row[0][2] + Row[2][0]) / s;
w = (Row[2][1] - Row[1][2]) / s;
}
else if(Row[1][1] > Row[2][2])
{
s = sqrt(1.0 + Row[1][1] - Row[0][0] - Row[2][2]) * 2.0; // S=4*qy
x = (Row[0][1] + Row[1][0]) / s;
y = 0.25 * s;
z = (Row[1][2] + Row[2][1]) / s;
w = (Row[0][2] - Row[2][0]) / s;
}
else
{
s = sqrt(1.0 + Row[2][2] - Row[0][0] - Row[1][1]) * 2.0; // S=4*qz
x = (Row[0][2] + Row[2][0]) / s;
y = (Row[1][2] + Row[2][1]) / s;
z = 0.25 * s;
w = (Row[1][0] - Row[0][1]) / s;
}

Orientation.
x = x;
Orientation.
y = y;
Orientation.
z = z;
Orientation.
w = w;

return true;
}
}//namespace glm
